This invention relates generally to processes and apparatus for estimating the values of signal parameters in the presence of noise and interference and for demodulating amplitude-, phase-, and frequency-modulated signals. More particularly, the invention relates to signal processors that utilize order statistics in performing the above functions.
Order statistics are a mature field within mathematical statistical analysis. These statistics are defined as follows. Let x.sub.1, x.sub.2, . . . , x.sub.N be samples from a continuously distributed process. Let y.sub.1 be the smallest of the x.sub.1, y.sub.2 be the next smallest, and so on through y.sub.N which is the largest of the x.sub.1. Then y.sub.1 is defined as the i'th order statistic of the random samples x.sub.1, x.sub.2, . . . , x.sub.N.
A familiar order statistic is the median. It is defined as y.sub.(N+1)/2 if N is odd and as the average of y.sub.N/2 and y.sub.1+N/2 if N is even. The maximum y.sub.N and the minimum y.sub.1 are also widely used.
Another statistic that is frequently desired is the mean which is defined as the sum over i of x.sub.i divided by N.
The recent literature has reported a significant number of applications requiring order statistics. For example, Gandhi et al. (Gandhi, P. P. and Kassam, S. A., "Design and Performance of Combination Filters for Signal Restoration", IEEE Transactions on Signal Processing, Jul., 1991) describe a class of non-linear moving-window filters that use rank order for the restoration of signals imbedded in additive white Gaussian noise. Haweel et al. (Haweel, Tarek I. and Clarkson, P. M., "A Class of Order Statistics LMS Algorithms", IEEE Transactions on Signal Processing, January, 1992) describe significant improvements to gradient-based adaptive filters using order statistics filtering of the gradient estimates. The field of image processing has long recognized the usefulness of order statistics filtering, as noted by Pratt (Pratt, William K., Digital Image Processing, pp. 330-333, John Wiley & Sons, 1978).
Additional applications have been reported by Nie and Unbehauen (Nie, X. and Unbehauen, R., "Edge Preserving Filtering by Combining Nonlinear Mean and Median Filters", IEEE Transactions on Signal Processing, November, 1991), Hwang (Hwang, J., "Systolic Architectures for Radar CFAR Detectors", IEEE Transactions on Signal Processing, October 1991), and Binenbaum et al. (Binenbaum, N. et al., "Neural Networks for Signal/Image Processing Using the Princeton Engine Multi-Processor", Proceedings of the IEEE Workshop on Neural Networks for Signal Processing, September 1991).
Order statistics can also be utilized to advantage in phase-lock-loop (PLL) and frequency-lock-loop (FLL) receivers that are found in virtually all modern communication systems. The rationale is that the theshold level for both PLL and FLL perforance is completely dominated by the onset of cycle slipping that is characterized as impulse noise. Order statistics filters, such as the median filter, should result in a significant extension of the threshold level and thereby improve receiver performance.
By extending the threshold level in phase and frequency lock loops the performance of virtually all communication links will be enhanced. The ability to remove non-Gaussian (as well as truly Gaussian) noise from baseband bit streams, without the level of inter-symbol interference normally associated with linear filters, could significantly improve a communication system's performance.
Potential improvements to magnetic storage devices (e.g. computer disks) also exist since the analog signal received from such devices suffers from impulse (or non-Gaussian) noise caused by magnetic drop-outs in the medium.
Until now, all implementations of true order statistic filters (also known as rank order processors) have been required to be digital. Ranking data in a moving window and selecting the sample having the desired rank for output is so very non-linear that digital methods were apparently the only feasible means of implementation. As a result, the usual hardware and bandwidth constraints normally associated with a digital processor were imposed.
There is a need for an order statistic processor which can perform the required processing in real time on wideband signals without the cost penalty imposed by high-speed digital processing approaches.